Chi-square distribution

The chi-square distribution is a continuous distribution that is specified by the degrees of freedom and the noncentrality parameter. The distribution is positively skewed, but skewness decreases with more degrees of freedom.

Test how well a sample fits a theoretical distribution. For example, you can use a chi-square goodness-of-fit test to determine whether your sample data fit a Poisson distribution.

Test the independence between categorical variables. For example, a manufacturer wants to know if the occurrence of four types of defects (missing pin, broken clamp, loose fastener, and leaky seal) is related to shift (day, evening, overnight).

When the degrees of freedom are 30 or more, the chi-square distribution can be reasonably approximated by a normal distribution, as illustrated by the following graphs: